Reference : Geometry of subelliptic diffusions |

Parts of books : Contribution to collective works | |||

Physical, chemical, mathematical & earth Sciences : Mathematics | |||

http://hdl.handle.net/10993/22438 | |||

Geometry of subelliptic diffusions | |

English | |

Thalmaier, Anton [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >] | |

2016 | |

Geometry, Analysis and Dynamics on sub-Riemannian Manifolds. Volume II | |

Barilari, Davide | |

Boscain, Ugo | |

Sigalotti, Mario | |

EMS Publishing House | |

EMS Series of Lectures in Mathematics (ELM) | |

85-169 | |

Yes | |

978-3-03719-163-7 | |

Zürich | |

Switzerland | |

[en] The lectures focus on some probabilistic aspects related to sub-Riemannian geometry. The main intention is to give an introduction to hypoelliptic and subelliptic diffusions. The notes are written from a geometric point of view trying to minimize the weight of ``probabilistic baggage'' necessary to follow the arguments. We discuss in particular the following topics: stochastic flows to second order differential operators; smoothness of transition probabilities under Hörmander's brackets condition; control theory and Stroock-Varadhan's support theorems; Malliavin calculus; Hörmander's theorem. The notes start from well-known facts in Geometric Stochastic Analysis and guide to recent on-going
research topics, like hypoelliptic heat kernel estimates; gradient estimates and Harnack type inequalities for subelliptic diffusion semigroups; notions of curvature related to sub-Riemannian diffusions. | |

Researchers ; Students | |

http://hdl.handle.net/10993/22438 | |

10.4171/163 | |

http://www.ems-ph.org/books/book.php?proj_nr=206&srch=series%7Celm | |

These are notes to a series of lectures given at the CIRM Summer School on "Sub-Riemannian manifolds: from geodesics to hypoelliptic diffusions"which took place at the Centre International de Rencontres Mathématiques in Marseille, as part of the IHP Trimester program "Geometry, Analysis and Dynamics on Sub-Riemannian manifolds" (Institut Henri Poincaré in Paris from Sept. 1 to Dec. 14, 2014). | |

FnR ; FNR7628746 > Anton Thalmaier > GEOMREV > Geometry of random evolutions > 01/03/2015 > 28/02/2018 > 2014 |

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